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XCVII. The Composition of Two Simple Harmonic Motions 

 exhibited by a Stretched String. By A. I. Steven", 

 M.A., B.Sc.) Assistant Lecturer and Demonstrator in 

 Physics, The University of Liverpool*. 



[Plate XVI.] 



I^HE compound character of a musical note emitted by a 

 stringed instrument may readily be demonstrated by 

 plucking the string, and then damping its motion at a con- 

 venient place, when only certain harmonics will still be heard. 

 It is, however, rather difficult to exhibit this phenomenon to 

 a large audience, and with a view to demonstrating the fact 

 that a string can vibrate in different ways and in them all 

 at one time, I have been led to devise the experiments 

 described in this paper. 



I propose to show how the composition of two Simple 

 Harmonic motions of different periods and amplitudes may 

 be exhibited (1) when the motions are in one plane, and (2) 

 when they are in perpendicular planes. 



I. Two vibrations in the same plane. 



A light silk cord, 3 or 4 metres long, is stretched horizon- 

 tally between two tuning forks A and B, electrically driven, 

 and placed so that their directions of motion are vertical. 

 The frequencies of the forks should be as low as possible, 

 and in the ratio a : b of the frequencies of the motions to 

 be compounded. The apparatus having been so far arranged, 

 proceed as follows : — Fix B in position and then set A 

 vibrating. Adjust the tension by pulling A out or pushing- 

 it in till the string is set in stationary vibration of large 

 amplitude with a loops in one plane. Unless the adjustment 

 is very carefully made a circular motion of the string may be 

 set up, which, of course, is not desired. Then let A be silenced 

 and set B vibrating, when the number of loops visible should 

 be b. Now set both forks vibrating, and each point on the 

 string will execute a vibration which is the resultant of the 

 two vibrations. 



The character of the vibration of the string is more clearly 

 seen with the aid of a stroboscopic wheel. The wheel 

 should have narrow radial slits, and it is desirable that it 

 should be controlled in such a manner that one slit passes 

 any fixed point once during a vibration of the string when 

 vibrating in one segment. (Professor Wilberforce's pattern 



* Communicated by the Author. 

 Phil. Mag. S. G. Vol. 2[). No. 138. June 1912. 3 S 



